Numerical calculations have been carried out to determine the temperature field due to the steady state hydrothermal flow of water through a smoothly curved cylindrical aquifer. It is found that the outflow water temperature relative to the ambient temperature at the base of the aquifer has a maximum at intermediate flow rates. If the flow velocity is low, the water cools by conduction to the wall rock before it reaches the surface; if the flow velocity is high, the water does not have time to be heated by conduction from the wall rock. The transition from laminar to turbulent flow reduces the flow through the aquifer and the temperature of the outflow water. It is found that the outflow temperatures are in general too low to explain continental hot springs. Our results show that shallow laminar hydrothermal flows are more effective in transporting heat to the surface than deeper turbulent flows. We suggest that very shallow (1--100 m) hydrothermal flows of seawater in the oceanic crust may be responsible for the reduction and variability of the measured near-surface geothermal gradient.